few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Thought: This activity asks students to reason how shapes can combine to make other shapes.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

1
options: Multiply and divide within 100.

Understand and apply properties of operations and the relationship between addition and subtraction.

Interpret the structure of expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Analyze patterns and relationships.

Work with radicals and integer exponents.

Represent and solve problems involving multiplication and division.

Use the four operations with whole numbers to solve problems.

Understand the relationship between zeros and factors of polynomials.

Work with equal groups of objects to gain foundations for multiplication.

Understand the connections between proportional relationships, lines, and linear equations.

Write and interpret numerical expressions.

Understand properties of multiplication and the relationship between multiplication and division.

Create equations that describe numbers or relationships

Perform arithmetic operations on polynomials.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Generate and analyze patterns.

Rewrite rational expressions.

Represent and solve problems involving addition and subtraction.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Add and subtract within 20.

Use properties of operations to generate equivalent expressions.

Write expressions in equivalent forms to solve problems.

Work with addition and subtraction equations.

Gain familiarity with factors and multiples.

Solve systems of equations.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Use polynomial identities to solve problems.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Represent and solve equations and inequalities graphically.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

Understand solving equations as a process of reasoning and explain the reasoning.
problem_activity: Activity
The purpose of this task is for students to rewrite rational numbers with terminating decimal expansions in fraction form and fractions with terminating decimal expansions as decimals. This activity is the first of a series of three in which students rewrite numbers in different ways, supporting their understanding of what rational and irrational numbers are and how they can be represented.
Monitor for students who write
\(\frac15\)
and
\(\frac{2}{10}\)
for 0.2.
Launch
Arrange students in groups of 2. Do not provide access to calculators.
Remind students that all rational numbers are fractions and their opposites, and they can all be written in the form
\(\frac{a}{b}\)
where
\(a\)
and
\(b\)
are integers (with
\(b\neq 0\)
). In fact, there are many equivalent fractions that represent a single rational number. For example, 5 is equivalent to
\(\frac{10}{2}\)
and
\(\frac{15}{3}\)
.
Students should complete the problems individually, then compare with their partners and come to resolutions over any differences. Repeat this process for the second problem.
Action and Expression: Internalize Executive Functions.
To support development of organizational skills, check in with students within the first 2-3 minutes of work time. Look for students who find equivalent ways to represent fractions and decimals. Check for precision in calculations and encourage partners to seek clarification in their discussions.
Supports accessibility for: Memory; Organization
Writing: MLR3 Clarify, Critique, Correct.
Present an incorrect statement that reflects a possible misunderstanding from the class. For example, finding the decimal representations of rational numbers, an incorrect statement is: “For finding the decimal representation of
\(\frac38\)
, divide 8 by 3 using long division ”. Prompt students to identify the error, and then write a correct version. This helps students evaluate, and improve on, the written mathematical arguments of others.
Design Principle(s): Maximize meta-awareness
Student Facing
Rational numbers are fractions and their opposites. All of these numbers are rational numbers. Show that they are rational by writing them in the form
\(\frac{a}{b}\)
or
\(\text -\frac{a}{b}\)
.
0.2
\(\text -\sqrt{4}\)
0.333
\(\sqrt[3]{1000}\)
-1.000001
\(\sqrt{\frac19}\)
All rational numbers have decimal representations, too. Find the decimal representation of each of these rational numbers.
\(\frac38\)
\(\frac75\)
\(\frac{999}{1000}\)
\(\frac{111}{2}\)
\(\sqrt[3]{\frac18}\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Some students may write that
\(0.333=\frac13\)
. If so, ask them to check their work by calculating the decimal representation of
\(\frac13\)
.
Activity Synthesis
The purpose of this discussion is to highlight different strategies for rewriting rational numbers in different forms. Select previously identified students to share their solutions, including one student who wrote
\(\frac15\)
for 0.2 and another who wrote
\(\frac{2}{10}\)
. For the problems with roots, the values were purposefully chosen to emphasize to students that just because a number is written with a square or cube root does not mean it is not rational.
For 0.2, draw a number line with the numbers 0, 1, and 2 with plenty of space between the integers. Subdivide the segment from 0 to 1 into 5 equal pieces, and then ask where to plot
\(\frac15\)
. Then label
\(\frac15\)
and ask how we can see that this is
\(\frac{2}{10}\)
. (Subdivide each fifth into two equal pieces—now each one is
\(\frac{1}{10}\)
.) Then label the point
\(\frac{2}{10}\)
and 0.2.
[IMG]
Remind students that the point corresponds to a rational number, and we have a lot of different ways we can represent that number.


correct_option_index: 6